Question: ${\sqrt[3]{3430} = \text{?}}$
Answer: $\sqrt[3]{3430}$ is the number that, when multiplied by itself three times, equals $3430$ First break down $3430$ into its prime factorization and look for factors that appear three times. So the prime factorization of $3430$ is $2\times 5\times 7\times 7\times 7$ Notice that we can rearrange the factors like so: $3430 = 2 \times 5 \times 7 \times 7 \times 7 = (7\times 7\times 7) \times 2\times 5$ So $\sqrt[3]{3430} = \sqrt[3]{7\times 7\times 7} \times \sqrt[3]{2\times 5}$ $\sqrt[3]{3430} = 7 \times \sqrt[3]{2\times 5}$ $\sqrt[3]{3430} = 7 \sqrt[3]{10}$